arXiv:1909.05140 · Physical review. B./Physical review. B

Momentum-space entanglement after a quench in one-dimensional disordered fermionic systems

Rex Lundgren, Fangli Liu, Pontus Laurell, Gregory A. Fiete

Published Dec 13, 2019• 13 citations

Abstract

We numerically investigate the momentum-space entanglement entropy and entanglement spectrum of the random-dimer model and its generalizations, which circumvent Anderson localization, after a quench in the Hamiltonian parameters. The type of dynamics that occurs depends on whether or not the Fermi level of the initial state is near the energy of the delocalized states present in these models. If the Fermi level of the initial state is near the energy of the delocalized states, we observe an interesting slow logarithmiclike growth of the momentum-space entanglement entropy followed by an eventual saturation. Otherwise, the momentum-space entanglement entropy is found to rapidly saturate. We also find that the momentum-space entanglement spectrum reveals the presence of delocalized states in these models for long times after the quench and the many-body entanglement gap decays logarithmically in time when the Fermi level is near the energy of the delocalized states.

DOI: 10.1103/physrevb.100.241108

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arXiv:1909.05140 · Physical review. B./Physical review. B

Momentum-space entanglement after a quench in one-dimensional disordered fermionic systems

Rex Lundgren, Fangli Liu, Pontus Laurell, Gregory A. Fiete

Published Dec 13, 2019• 13 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.100.241108

Related papers

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We investigate the growth of the entanglement entropy

{S}_{\mathrm{ent}}

following global quenches in two-dimensional free fermion models with potential and bond disorder. For the potential disorder case, we show that an intermediate weak localization regime exists in which

{S}_{\mathrm{ent}}(t)

grows logarithmically in time

t

before Anderson localization sets in. For the case of binary bond disorder near the percolation transition, we find additive logarithmic corrections to area and volume laws as well as a scaling at long times, which is consistent with an infinite randomness fixed point.

L

as $S(L,t\ensuremath{\rightarrow}\ensuremath{\infty})\ensuremath{\sim}lnL$. We further study the interplay of long-range hopping and interactions on the growth of entanglement and the many-body localization (MBL) transition in this system. We develop an analogy to higher-dimensional short-range systems to compare and contrast such behavior with the physics of MBL in a higher dimension.

{S}_{N}(t)

for the disordered Heisenberg chain and show that this behavior is not transient and persists even for very strong disorder. Calculating the truncated R\'enyi number entropy ${S}_{N}^{(\ensuremath{\alpha})}(t)={(1\ensuremath{-}\ensuremath{\alpha})}^{\ensuremath{-}1}ln{\ensuremath{\sum}}_{n}{p}^{\ensuremath{\alpha}}(n)$ for $\ensuremath{\alpha}\ensuremath{\ll}1$ and

p(n)>{p}_{c}

---which is sensitive to large number fluctuations occurring with low probability---we demonstrate that the particle number distribution

p(n)

in one half of the system has a continuously growing tail. This indicates a slow but steady increase in the number of particles crossing between the partitions in the interacting case and is in sharp contrast to Anderson localization for which we show that ${S}_{N}^{(\ensuremath{\alpha}\ensuremath{\rightarrow}0)}(t)$ saturates for any cutoff

{p}_{c}>0

. We show, furthermore, that the growth of

{S}_{N}

is not the consequence of rare states or rare regions but rather represents typical behavior. These findings indicate that the interacting system is never fully localized even for very strong but finite disorder.